@phdthesis{Schelter2012,
  author    = {Schelter, J{\"o}rg},
  title     = {The Aharonov-Bohm effect and resonant scattering in graphene},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-74662},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {In this thesis, the electronic transport properties of mesoscopic condensed matter systems based on graphene are investigated by means of numerical as well as analytical methods. In particular, it is analyzed how the concepts of quantum interference and disorder, which are essential to mesoscopic devices in general, are affected by the unique electronic and transport properties of the graphene material system. We consider the famous Aharonov-Bohm effect in ring-shaped transport geometries, and, besides providing an overview over the recent developments on the subject, we study the signatures of fundamental phenomena such as Klein tunneling and specular Andreev reflection, which are specific to graphene, in the magnetoconductance oscillations. To this end, we introduce and utilize a variant of the well-known recursive Green's function technique, which is an efficient numerical method for the calculation of transport observables in effectively non-interacting open quantum systems in the framework of a tight binding model. This technique is also applied to study the effects of a specific kind of disorder, namely short-range resonant scatterers, such as strongly bound adatoms or molecules, that can be modeled as vacancies in the graphene lattice. This numerical analysis of the conductance in the presence of resonant scatterers in graphene leads to a non-trivial classification of impurity sites in the graphene lattice and is further substantiated by an independent analytical treatment in the framework of the Dirac equation. The present thesis further contains a formal introduction to the topic of non-equilibrium quantum transport as appropriate for the development of the numerical technique mentioned above, a general introduction to the physics of graphene with a focus on the particular phenomena investigated in this work, and a conclusion where the obtained results are summarized and open questions as well as potential future developments are highlighted.},
  subject      = {Graphen},
  language  = {en}
}
@phdthesis{Fuchs2016,
  author    = {Fuchs, Moritz Jakob},
  title     = {Spin dynamics in the central spin model: Application to graphene quantum dots},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-136079},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2016},
  abstract  = {Due to their potential application for quantum computation, quantum dots have attracted a lot of interest in recent years. In these devices single electrons can be captured, whose spin can be used to define a quantum bit (qubit). However, the information stored in these quantum bits is fragile due to the interaction of the electron spin with its environment. While many of the resulting problems have already been solved, even on the experimental side, the hyperfine interaction between the nuclear spins of the host material and the electron spin in their center remains as one of the major obstacles. As a consequence, the reduction of the number of nuclear spins is a promising way to minimize this effect. However, most quantum dots have a fixed number of nuclear spins due to the presence of group III and V elements of the periodic table in the host material. In contrast, group IV elements such as carbon allow for a variable size of the nuclear spin environment through isotopic purification. Motivated by this possibility, we theoretically investigate the physics of the central spin model in carbon based quantum dots. In particular, we focus on the consequences of a variable number of nuclear spins on the decoherence of the electron spin in graphene quantum dots. Since our models are, in many aspects, based upon actual experimental setups, we provide an overview of the most important achievements of spin qubits in quantum dots in the first part of this Thesis. To this end, we discuss the spin interactions in semiconductors on a rather general ground. Subsequently, we elaborate on their effect in GaAs and graphene, which can be considered as prototype materials. Moreover, we also explain how the central spin model can be described in terms of open and closed quantum systems and which theoretical tools are suited to analyze such models. Based on these prerequisites, we then investigate the physics of the electron spin using analytical and numerical methods. We find an intriguing thermal flip of the electron spin using standard statistical physics. Subsequently, we analyze the dynamics of the electron spin under influence of a variable number of nuclear spins. The limit of a large nuclear spin environment is investigated using the Nakajima-Zwanzig quantum master equation, which reveals a decoherence of the electron spin with a power-law decay on short timescales. Interestingly, we find a dependence of the details of this decay on the orientation of an external magnetic field with respect to the graphene plane. By restricting to a small number of nuclear spins, we are able to analyze the dynamics of the electron spin by exact diagonalization, which provides us with more insight into the microscopic details of the decoherence. In particular, we find a fast initial decay of the electron spin, which asymptotically reaches a regime governed by small fluctuations around a finite long-time average value. Finally, we analytically predict upper bounds on the size of these fluctuations in the framework of quantum thermodynamics.},
  subject      = {Elektronenspin},
  language  = {en}
}
@phdthesis{Boettcher2021,
  author    = {B{\"o}ttcher, Jan Frederic},
  title     = {Fate of Topological States of Matter in the Presence of External Magnetic Fields},
  doi       = {10.25972/OPUS-22045},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-220451},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2021},
  abstract  = {The quantum Hall (QH) effect, which can be induced in a two-dimensional (2D) electron gas by an external magnetic field, paved the way for topological concepts in condensed matter physics. While the QH effect can for that reason not exist without Landau levels, there is a plethora of topological phases of matter that can exist even in the absence of a magnetic field. For instance, the quantum spin Hall (QSH), the quantum anomalous Hall (QAH), and the three-dimensional (3D) topological insulator (TI) phase are insulating phases of matter that owe their nontrivial topology to an inverted band structure. The latter results from a strong spin-orbit interaction or, generally, from strong relativistic corrections. The main objective of this thesis is to explore the fate of these preexisting topological states of matter, when they are subjected to an external magnetic field, and analyze their connection to quantum anomalies. In particular, the realization of the parity anomaly in solid state systems is discussed. Furthermore, band structure engineering, i.e., changing the quantum well thickness, the strain, and the material composition, is employed to manipulate and investigate various topological properties of the prototype TI HgTe. Like the QH phase, the QAH phase exhibits unidirectionally propagating metallic edge channels. But in contrast to the QH phase, it can exist without Landau levels. As such, the QAH phase is a condensed matter analog of the parity anomaly. We demonstrate that this connection facilitates a distinction between QH and QAH states in the presence of a magnetic field. We debunk therefore the widespread belief that these two topological phases of matter cannot be distinguished, since they are both described by a \$\mathbb{Z}\$ topological invariant. To be more precise, we demonstrate that the QAH topology remains encoded in a peculiar topological quantity, the spectral asymmetry, which quantifies the differences in the number of states between the conduction and valence band. Deriving the effective action of QAH insulators in magnetic fields, we show that the spectral asymmetry is thereby linked to a unique Chern-Simons term which contains the information about the QAH edge states. As a consequence, we reveal that counterpropagating QH and QAH edge states can emerge when a QAH insulator is subjected to an external magnetic field. These helical-like states exhibit exotic properties which make it possible to disentangle QH and QAH phases. Our findings are of particular importance for paramagnetic TIs in which an external magnetic field is required to induce the QAH phase. A byproduct of the band inversion is the formation of additional extrema in the valence band dispersion at large momenta (the `camelback'). We develop a numerical implementation of the \$8 \times 8\$ Kane model to investigate signatures of the camelback in (Hg,Mn)Te quantum wells. Varying the quantum well thickness, as well as the Mn-concentration, we show that the class of topologically nontrivial quantum wells can be subdivided into direct gap and indirect gap TIs. In direct gap TIs, we show that, in the bulk \$p\$-regime, pinning of the chemical potential to the camelback can cause an onset to QH plateaus at exceptionally low magnetic fields (tens of mT). In contrast, in indirect gap TIs, the camelback prevents the observation of QH plateaus in the bulk \$p\$-regime up to large magnetic fields (a few tesla). These findings allowed us to attribute recent experimental observations in (Hg,Mn)Te quantum wells to the camelback. Although our discussion focuses on (Hg,Mn)Te, our model should likewise apply to other topological materials which exhibit a camelback feature in their valence band dispersion. Furthermore, we employ the numerical implementation of the \$8\times 8\$ Kane model to explore the crossover from a 2D QSH to a 3D TI phase in strained HgTe quantum wells. The latter exhibit 2D topological surface states at their interfaces which, as we demonstrate, are very sensitive to the local symmetry of the crystal lattice and electrostatic gating. We determine the classical cyclotron frequency of surface electrons and compare our findings with experiments on strained HgTe.},
  subject      = {Topologie},
  language  = {en}
}
@phdthesis{Posske2015,
  author    = {Posske, Thore Hagen},
  title     = {Dressed Topological Insulators: Rashba Impurity, Kondo Effect, Magnetic Impurities, Proximity-Induced Superconductivity, Hybrid Systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-131249},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {Topological insulators are electronic phases that insulate in the bulk and accommodate a peculiar, metallic edge liquid with a spin-dependent dispersion. They are regarded to be of considerable future use in spintronics and for quantum computation. Besides determining the intrinsic properties of this rather novel electronic phase, considering its combination with well-known physical systems can generate genuinely new physics. In this thesis, we report on such combinations including topological insulators. Specifically, we analyze an attached Rashba impurity, a Kondo dot in the two channel setup, magnetic impurities on the surface of a strong three-dimensional topological insulator, the proximity coupling of the latter system to a superconductor, and hybrid systems consisting of a topological insulator and a semimetal. Let us summarize our primary results. Firstly, we determine an analytical formula for the Kondo cloud and describe its possible detection in current correlations far away from the Kondo region. We thereby rely on and extend the method of refermionizable points. Furthermore, we find a class of gapless topological superconductors and semimetals, which accommodate edge states that behave similarly to the ones of globally gapped topological phases. Unexpectedly, we also find edge states that change their chirality when affected by sufficiently strong disorder. We regard the presented research helpful in future classifications and applications of systems containing topological insulators, of which we propose some examples.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Goth2015,
  author    = {Goth, Florian},
  title     = {Continuous time quantum Monte Carlo Studies of Quenches and Correlated Systems with Broken Inversion Symmetry},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-118836},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {This thesis deals with quantum Monte Carlo simulations of correlated low dimensional electron systems. The correlation that we have in mind is always given by the Hubbard type electron electron interaction in various settings. To facilitate this task, we develop the necessary methods in the first part. We develop the continuous time interaction expansion quantum algorithm in a manner suitable for the treatment of effective and non-equilibrium problems. In the second part of this thesis we consider various applications of the algorithms. First we examine a correlated one-dimensional chain of electrons that is subject to some form of quench dynamics where we suddenly switch off the Hubbard interaction. We find the light-cone-like Lieb-Robinson bounds and forms of restricted equilibration subject to the conserved quantities. Then we consider a Hubbard chain subject to Rashba spin-orbit coupling in thermal equilibrium. This system could very well be realized on a surface with the help of metallic adatoms. We find that we can analytically connect the given model to a model without spin-orbit coupling. This link enabled us to interpret various results for the standard Hubbard model, such as the single-particle spectra, now in the context of the Hubbard model with Rashba spin-orbit interaction. And finally we have considered a magnetic impurity in a host consisting of a topological insulator. We find that the impurity still exhibits the same features as known from the single impurity Anderson model. Additionally we study the effects of the impurity in the bath and we find that in the parameter regime where the Kondo singlet is formed the edge state of the topological insulator is rerouted around the impurity.},
  subject      = {Elektronenkorrelation},
  language  = {en}
}